How to Add Fractions With Unlike Denominators

Adding fractions is one of the first math skills that feels different from whole-number arithmetic. The key is simple: fractions must describe equal-sized pieces before you can combine them.

Quick idea

A denominator names the size of the pieces. You can only add the numerators after both fractions use the same denominator.

Steps

1. Find a common denominator. The least common denominator is best, but any shared multiple works.
2. Rewrite each fraction as an equivalent fraction with that denominator.
3. Add the numerators and keep the denominator the same.
4. Simplify the answer if the numerator and denominator share a factor.

Worked example

Add one third and one fourth.

Full solution

Step-by-step walkthrough

Step 1

The denominators are 3 and 4, so use 12 as the common denominator.

Step 2

One third becomes four twelfths, and one fourth becomes three twelfths.

Step 3

Add 4 plus 3 to get 7 twelfths.

Common mistake

Do not add the denominators. One third plus one fourth is not two sevenths because thirds and fourths are different-sized pieces.

Practice problems

1. Add 1/2 + 1/3.
2. Add 2/5 + 1/10.
3. Add 3/4 + 2/3.

Answers

1. 5/6
2. 1/2
3. 17/12 or 1 5/12

Ask Pennpaper to explain it live

If the steps make sense but you still feel stuck, start a Pennpaper lesson and ask the tutor to draw the problem on the whiteboard. Seeing the symbols move step by step is often what makes the concept click.

Related guides

• How to Subtract Fractions Step by Step
• How to Multiply Fractions
• How to Convert Fractions to Decimals